Karl Pearson 
255 
From this equation the squared standard deviations of the arrays were calculated 
with the following results, the unit being 2 mms. : 
Age array 
Squared Standard Deviation 
Age array 
Squared Standard Deviation 
Observed 
Calculated 
Observed 
Calculated 
3—4 
[0?] 
6-8194 
13—14 
11-2822 
11-1865 
4—5 
8-3250 
7-2561 
14—15 
12-8630 
11-6232 
5—6 
8-5708 
7-6929 
15—16 
120152 
12-0599 
6—7 
8-7859 
8-1296 
16—17 
14-9738 
12-4966 
7—8 
8-9293 
8-5663 
17—18 
10-0356 
12-9333 
8—9 
6-9517 
90030 
18—19 
9-7563 
13-3700 
9—10 
11-4765 
9-4397 
19—20 
23-4314 
13-S067 
10—11 
8-7930 
9-8764 
20—21 
6-4065 
14-24"4 
11—12 
10-2970 
10-3131 
2] 22 
17-1512 
14-6801 
12—13 
10-2791 
10-7498 
22 23 
[-9166?] 
15-1169 
The calculated results give a reasonable graduation of the somewhat erratic observed 
values, and these values were used in evaluating the formula 
The following table now gives all the required data for the calculation of x^> 
and we deduce ^ = 9-5845 corresponding to P = -974: for n = 20 + 1 = 21 as 
argument. 
Regression Curve for Girls^ Auricular Height with Age. 
Age group 
"V* 
{"'). - '"„)"* 
"p 
3—4 
1-5 
3-4987 
115-25 
116-90 
2-7225 
6-8191 
1-3968 
4—5 
7-5 
9-4934 
116-96 
117-66 
-4900 
7-2561 
-6411 
5—6 
19 
20-9833 
117-47 
118-42 
•9025 
7-6929 
2-4617 
6—7 
41-5 
43-4635 
11910 
119-24 
-0196 
8-1296 
•1048 
7-8 
76 
77-9331 
120-30 
120-03 
-0484 
8-5663 
-4403 
8—9 
123-5 
125-3913 
121-63 
120-93 
-4900 
90030 
6-8246 
9—10 
178 
179-8433 
121-72 
121-78 
-0036 
9-4397 
-068(j 
10—11 
227-5 
229-2997 
122-82 
1 22-62 
-0400 
9-8764 
-9287 
11—12 
265-5 
267-2663 
123-14 
123-42 
-0784 
10-3131 
2-0318 
12—13 
282-5 
284-2513 
123-89 
124-18 
-0841 
10-7498 
2-2238 
13—14 
275 
276-7579 
124-86 
124-88 
•0004 
11-1865 
-0099 
14—15 
246 
247-7834 
125-71 
125-52 
•0361 
11-6232 
-7696 
15—16 
197 
198-8266 
126-16 
126-07 
-0081 
12-0599 
•1335 
16—17 
143-5 
145-3737 
126-53 
126-52 
-0001 
12-4966 
-0012 
17—18 
91-5 
93-4195 
126-91 
126-87 
•0016 
12-9333 
■0116 
18—19 
53 
54-9533 
127-02 
127 09 
■0049 
13-3700 
-0201 
19—20 
26 
27-9771 
129-56 
127-18 
5-6644 
13-8067 
11-4780 
20—21 
9 
10-9921 
123-82 
127-11 
10-8241 
14-2434 
8-3533 
21—22 
7 
8-9938 
126-50 
126-88 
•1444 
14-6801 
-0885 
22—23 
1-5 
3-4987 
125-25 
126-48 
1-5129 
15- 1169 
-3502 
2272 
Total 
^'2 = 38-3381 
9-5845 
True X 
* In millimetre units. For values of w,, and »(,, (cubic (c)) see loc. cii. p. 37. 
t In 2 millimetre units. Hence as given above must be divided by four, to obtain true value. 
